Question

the radius and the slant height of cone are in the ratio 7:25. if it's curved surface area is 26950cm square find its vertical height

Answer 1

GIVEN :
Curved surface area of Cone = 26950 cm²
Radius (r): slant height (h)= 7 :25
Let the radius of a Cone = 7x & slant Height of a Cone = 25x
Curved surface area of Cone = πrl
26950 = 22/7 × 7x × 25x
26950 = 22 × 25x²
x² = 26950 / 22×25 = 1078/22 = 49
x =√49
x = 7 cm
Radius (r) = 7x = 7 × 7 = 49 cm
Slant Height (l) = 25x = 25 × 7 = 175 cm
Slant Height (l) of Cone = √r² +h²
l² = r² +h²
(175)² = (49)² + h²
175² - 49² = h²
h² = (175+49) (175-49)
[a² - b² = (a+b) (a-b)]
h² = 224 × 126 = 28224
h =√28224
h = 168 cm
Hence, the vertical height of a Cone is 168 cm.

HOPE THIS WILL HELP YOU...

Answer 2

Heya !!

⚫ Given :- The radius and slant height of cone are in 7:25 ratio.
C.S.A. of Cone = 26950cm^2

⚫ To Find :- Height of the cone.( h )

⚫ Solution :- Let the radius ( r ) = 7x
Slant height ( l ) = 25x

C.S.A of cone = πrl

26950 = 22/7 × 7x × 25x

26950 = 22 × 25x^2

26950 = 550x^2

26950/550 = x^2

49 = x^2

x = √49

x = 7

Put value of ( x ) in radius and slant height.

radius ( r ) = 7x = 7 ( 7 ) = 49cm
slant height ( l ) = 25x = 25 ( 7 ) = 175cm

We know, h^2 + r^2 = l^2

h^2 = l^2 - r^2
h^2 = ( 175 )^2 - ( 49 )^2
h^2 = 30625 - 2401
h^2 = 28224
h = √28224
h = 168 cm


Hence, Height of cone is 168cm.


Hope it helps you..

Thanks .. (: